Related papers: Theta-functions on the Kodaira-Thurston manifold

In this article we investigate the Duistermaat-Heckman theorem using the theory of hyperfunctions. In applications involving Hamiltonian torus actions on infinite dimensional manifolds, this more general theory seems to be necessary in…

We consider a Hamiltonian torus action on a compact connected symplectic manifold M. For a certain class of Lagrangian submanifolds Q of M we show that the image of Q under the momentum map is convex. As an application we complete the…

Let $G$ be a complex reductive algebraic group with Lie algebra $\mathfrak{g}$ and let $G_{\mathbb{R}}$ be a real form of $G$ with maximal compact subgroup $K_{\mathbb{R}}$. Associated to $G_{\mathbb{R}}$ is a $K \times…

In this paper, we introduce the notion of maximal actions of compact tori on smooth manifolds and study compact connected complex manifolds equipped with maximal actions of compact tori. We give a complete classification of such manifolds,…

Following McDuff and Tolman's work on toric manifolds [McDT06], we focus on 4-dimensional NEF toric manifolds and we show that even though Seidel's elements consist of infinitely many contributions, they can be expressed by closed formulas.…

Quantum theta functions were introduced by the author in [Ma1]. They are certain elements in the function rings of quantum tori. By definition, they satisfy a version of the classical functional equations involving shifts by the…

Let $\mathbf{G}$ be a unipotent group scheme defined in terms of a nilpotent Lie lattice over the ring $\mathcal{O}$ of integers of a number field. We consider bivariate zeta functions of groups of the form $\mathbf{G}(\mathcal{O})$…

Under some suitable assumptions Riemannian manifolds $(M, g, H)$ that admit a connection $\hat\nabla$ with torsion a 3-form $H$, which is both closed $d H=0$ and $\hat\nabla$-covariantly constant, are locally isometric to a product $N\times…

In this present paper we study geometry of compact complex manifolds equipped with a \emph{maximal} torus $T=(S^1)^k$ action. We give two equivalent constructions providing examples of such manifolds given a simplicial fan $\Sigma$ and a…

The pro-isomorphic zeta function of a torsion-free finitely generated nilpotent group G enumerates finite index subgroups H such that H and G have isomorphic profinite completions. It admits an Euler product decomposition, indexed by the…

Let M be a Kaehler manifold with a free, holomorphic and Hamiltonian action of the standard n-torus T. We give a simple, explicit and canonical formula for the Kaehler potential on the Kaehler reduction of M. As a consequence we can derive…

We prove that the tau-function of the integrable discrete sine-Gordon model apart from the "standard" bilinar identities obeys a number of "non-standard" ones. They can be combined into a bivector 3-dimensional difference equation which is…

We express the zeta function associated to the Laplacian operator on $S^1_r\times M$ in terms of the zeta function associated to the Laplacian on $M$, where $M$ is a compact connected Riemannian manifold. This gives formulas for the…

Let a torus $T$ act on a symplectic manifold $(M,\omega)$ with moment map $\phi$. We say that the Hamiltonian $T$-manifold $(M,\omega,\phi)$ has complexity one if $\frac{1}{2} \dim M - \dim T = 1$, and that it is K\"ahler if it admits an…

Let G be an n-dimensional torus and $\tau$ a Hamiltonian action of G on a compact symplectic manifold, M. If M is pre-quantizable one can associate with $\tau$ a representation of G on a virtual vector space, Q(M), by…

In the 80's Kudla and Millson introduced a theta function in two variables. It behaves as a Siegel modular form with respect to the first variable, and is a closed differential form on an orthogonal Shimura variety with respect to the other…

We study representation zeta functions of finitely generated, torsion-free nilpotent groups which are rational points of unipotent group schemes over rings of integers of number fields. Using the Kirillov orbit method and p-adic…

We show that the theta representations on certain covers of general linear groups support certain types of unique functionals. The proof involves two types of Fourier coefficients. The first are semi-Whittaker coefficients, which generalize…

Given a compact symplectic toric manifold $(M,\omega, \mathbb{T})$, we identify a class $DGK_{\omega}^{\mathbb{T}}(M)$ of $\mathbb{T}$-invariant generalized K\"ahler structures for which a generalisation the Abreu-Guillemin theory of toric…

Motivated by recent proposals relating non-supersymmetric Type 0A theory to M-theory compactified on a singular wedge geometry, we study an M-theory compactification on a seven-manifold with G_2 structure, realized as a deformed K3…